# How do you find #int (x+4)/(x^2+2x+5) dx# using partial fractions?

Since we are requested to use partial fractions to solve this, I guess the hope is that we can simplify the integrand.

They say fools rush in where angels fear to tread, so here I go...

So:

Using Heaviside's cover up method, we find:

So:

Use:

So:

Hence:

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To find the integral (\int \frac{x + 4}{x^2 + 2x + 5} , dx) using partial fractions, you first decompose the fraction into simpler fractions. Then you solve for the coefficients of the partial fractions by equating the original expression with the decomposition. After finding the coefficients, you integrate each partial fraction separately.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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